Missing properties in properties window
Most tabs in the properties panel are only displayed if the active object is a certain type. If there is no active object, most of them will be hidden, as you have discovered. It's a bit uncommon to have no active object, but it is possible; deleting all objects in the scene, or creating a new empty scene are two ways. It's also possible to set it in python (bpy.context.scene.objects.active = None), and indeed some addons will (intentionally or otherwise) introduce such a state.

Similarly, not all modifiers can be applied to curve objects. Hence, not all modifiers are available in the drop down while a curve object is selected.